nteractive  oncept  ping in  (iCMap) Martin Homik, Erica Melis, Philipp Kärger -- ActiveMath Group – Delfi 2005, Rostock G...
Motivation <ul><li>Concept Maps: </li></ul><ul><li>Understanding of structures and dependencies </li></ul><ul><li>Support ...
Not a Concept Map Fraction calculation Subtraction Addition Multiplication Parts of units Integer Extension Mixed number D...
Not a Concept Map
A Concept Map
iCMap (CoolModes plugin)
iCMap (CoolModes plugin)
Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level...
Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level...
Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level...
Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content Concept level...
iCMap Feedback
iCMap Feedback
Local Feedback
Verification <ul><li>Against knowledge base </li></ul><ul><li>Against authored exercise </li></ul><ul><li>Deduction </li><...
Deductive Relation: Transitivity <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content conce...
Deductive Relation: Transitivity <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content conce...
Deductive Relation: Equivalence <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concep...
Fault Tolerance <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></...
ActiveMath Architecture mBase Web Server Session Manager Presentation Generator (XSLT) XML-RPC Java http User Model Histor...
Conclusion <ul><li>Concept maps: support (meta-)cognitive skills </li></ul><ul><li>Mathematics is a huge concept map itsel...
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Interactive Concept Mapping in ActiveMath (iCMap)

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Describes a tool for conept mapping in mathematics that offers feedback, evaluation, and suggestions. It is part of the ActiveMath learning environment.

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  • Maximale Dauer: 30 Minuten inklusive Diskussion. Pädagogen verwenden eher Mindmaps: Assoziatives Netzwerk Thematische Nähe Concept Maps: Unterstützen Analyse und Reflektion Hierarchisch geordnetes Netzwerk von Begriffen Inhaltliche und logische Beziehungen
  • Interactive Concept Mapping in ActiveMath (iCMap)

    1. 1. nteractive oncept ping in (iCMap) Martin Homik, Erica Melis, Philipp Kärger -- ActiveMath Group – Delfi 2005, Rostock German Research Center for Artificial Intelligence (DFKI GmbH) University of Saarland I C Map
    2. 2. Motivation <ul><li>Concept Maps: </li></ul><ul><li>Understanding of structures and dependencies </li></ul><ul><li>Support analysis and reflection skills </li></ul><ul><li>Mathematics has well defined concepts </li></ul><ul><li>School teachers use intuitive mind maps </li></ul><ul><li>No tools for concept mapping in math </li></ul><ul><li>iCMap: </li></ul><ul><li>Integrated into ActiveMath learning environment </li></ul><ul><li>Mathematical knowledge base and ontology </li></ul><ul><li>Interactivity </li></ul><ul><li>Feedback </li></ul><ul><li>Author support </li></ul>
    3. 3. Not a Concept Map Fraction calculation Subtraction Addition Multiplication Parts of units Integer Extension Mixed number Division Reduction <ul><li>Nominator * Nominator, </li></ul><ul><li>Denominator * Denominator </li></ul><ul><li>Reduction </li></ul><ul><li>Create mixed number if possible </li></ul><ul><li>Multiply first fraction with the second fraction’s reciprocal </li></ul><ul><li>Common denominator </li></ul><ul><ul><li>Add nominators </li></ul></ul><ul><li>No common denominator </li></ul><ul><ul><li>Find common denominator </li></ul></ul><ul><ul><li>Add nominators </li></ul></ul><ul><li>Reduction </li></ul><ul><li>Create mixed number if possible </li></ul><ul><li>Common denominator </li></ul><ul><ul><li>Subtract nominators </li></ul></ul><ul><li>No common denominator </li></ul><ul><ul><li>Find common denominator </li></ul></ul><ul><ul><li>Subtract nominators </li></ul></ul><ul><li>Reduction </li></ul><ul><li>Create mixed number if possible </li></ul><ul><li>by a give number </li></ul><ul><li>as far as possible over the fraction line </li></ul><ul><li>Transform fractions into mixed number </li></ul><ul><li>Transform mixed number into fractions </li></ul><ul><li>with given number </li></ul><ul><li>Basic times table </li></ul><ul><li>Prime numbers </li></ul><ul><li>Square numbers </li></ul><ul><li>Prime factor decomposition </li></ul><ul><li>Multiple </li></ul><ul><li>Factor </li></ul><ul><li>Factor diagrams </li></ul><ul><li>Highest common factor </li></ul><ul><li>Least common multiple </li></ul>
    4. 4. Not a Concept Map
    5. 5. A Concept Map
    6. 6. iCMap (CoolModes plugin)
    7. 7. iCMap (CoolModes plugin)
    8. 8. Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3
    9. 9. Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for for for for for for for for for
    10. 10. Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for for Domain prerequisite Domain prerequisite Domain prerequisite
    11. 11. Knowledge Representation <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content Concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for against isA
    12. 12. iCMap Feedback
    13. 13. iCMap Feedback
    14. 14. Local Feedback
    15. 15. Verification <ul><li>Against knowledge base </li></ul><ul><li>Against authored exercise </li></ul><ul><li>Deduction </li></ul>
    16. 16. Deductive Relation: Transitivity <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 isA isA isA
    17. 17. Deductive Relation: Transitivity <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 Domain prerequisite Domain prerequisite Domain prerequisite
    18. 18. Deductive Relation: Equivalence <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 isA isA for for equivalence equivalence
    19. 19. Fault Tolerance <ul><li>Abstract concept level: </li></ul><ul><li>Symbols </li></ul><ul><li>Content concept level: </li></ul><ul><li>Definitions </li></ul><ul><li>Theorems </li></ul><ul><li>Satellite level: </li></ul><ul><li>Examples </li></ul><ul><li>Exercises </li></ul>S 1 S 2 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for isA isA for for for
    20. 20. ActiveMath Architecture mBase Web Server Session Manager Presentation Generator (XSLT) XML-RPC Java http User Model History Profile JNLP (http)
    21. 21. Conclusion <ul><li>Concept maps: support (meta-)cognitive skills </li></ul><ul><li>Mathematics is a huge concept map itself </li></ul><ul><li>iCMap: </li></ul><ul><ul><li>Integrated into ActiveMath learning environment </li></ul></ul><ul><ul><li>Mathematical ontology and knowledge base </li></ul></ul><ul><ul><li>Interactivity, Feedback, Hints </li></ul></ul><ul><ul><li>Supports self-responsible and explorative learning </li></ul></ul><ul><li>Evaluation: </li></ul><ul><ul><li>Till end of 2005 at school and university </li></ul></ul>
    22. 22. Thank you!

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